Japanese crosswords(scanwords) are encoded images. Player Challenge and Goal logic game- solve this image.
The coding goes like this. Let's say we have an image:
For each line, we count the lengths of the shaded segments and write these numbers next to the corresponding stripes:
Now we repeat the same operation for the scanword columns and write the corresponding sets of numbers above the columns:
Now we remove the image and leave only the numbers. This is a ready-made Japanese crossword puzzle:
The player's task is to reconstruct the picture using only numbers.
General logic and tactics for solving Japanese crosswords
The logic is very simple. You need to find horizontal lines or vertical columns where you can draw some conclusion about which cells are shaded and which are not shaded. You display these logical conclusions with labels. As you receive more and more new clues, you move further and further until the crossword puzzle is completely solved.
Let's now look at some techniques
Where to start solving a Japanese crossword puzzle
At first, the scanword is not filled in. For now you only know the numbers. Let's see what you can do in this situation.
The simplest techniques: solving at first sight
As you have seen, there are times when you can definitely tell how a row is filled. For example:
can be filled in only one way - all cells are painted over.
A slightly less obvious case:
turns out to be just as simple and unambiguous:
But such situations do not occur often.
Partial solution of the crossword puzzle at a glance
Often a row or column cannot be fully figured out right away, but we can still draw some conclusions about how it is filled.
Let's look at an example:
There are three possible filling options:
As you can see, in all these options the third cell is painted over. From this we can conclude: “We don’t know exactly how this row is filled, but the third cell in it is definitely filled”:
A similar approach works in more complex logical problems. Example:
The following options are possible here:
and we can conclude that there are as many as four filled cells in the scanword:
We have not solved the series completely, but we have received quite a bit of information. Let's now see how to use it and continue solving it.
How to continue solving a crossword puzzle using incomplete information.
So. Do you already know something about how to clarify these conclusions and get closer to a complete solution?
Let's introduce one more notation. We will denote with the symbol “✕” those positions that we know for sure that they are not shaded.
Such information is also very valuable when solving.
You know something is painted over
If you already know that some cell in a row/column is shaded, then you can often conclude that some cells are definitely not shaded.
The simplest case is when there is only one strip in a row. Let's say you have this situation:
We already know that one cell must be painted over. And we are left with only three options:
That is, we can say with confidence that the two outermost cells on each side are definitely not painted:
If there is more than one colored stripe in a row/column, then the situation becomes more complicated, but even here a conclusion can be drawn.
Consider this example:
At first glance, the shaded cell may be part of either of the two stripes, and we cannot say anything definite. But if you look closely, it becomes clear that a strip of two cells cannot be located to the right of the shaded cell. After all, then they will stick together and there will no longer be two cells in the strip. This means that the rightmost cell is definitely empty:
And applying the knowledge from the previous presentation, we can draw a conclusion about two more cells:
And this is already very good.
You know something is not painted over
At the previous step, we began to see cells that we know for sure that they are not painted over. This is very useful information and very easy to use.
Very often you can infer other unfilled cells. Let's look at an example:
Here all the strips have a length of 2, which means none of them can fit to the right of an unfilled cell. This means that the rightmost cell is not painted over.
And of course, we can draw a conclusion about two more cells, using the techniques described above (by considering all the options for the location of the shaded stripes, and highlighting the cells that turn out to be shaded in any case):
We found out the color of three cells in the scanword puzzle.
Let's consider another logical technique.
Unfilled cells divide the line/column into segments, and quite often it is possible to determine which segments contain which stripes. Look at the example:
For convenience, I designated the segments with letters of the Latin alphabet.
It is clear that segment A is empty, since it cannot contain a segment of four shaded cells. Conclusion one:
Two two-cell segments cannot fit into segment D (otherwise they will “stick together”). This means that each of our three segments occupies one of the three remaining segments. We can draw the following conclusions about the first two segments:
Overall, we have made good progress.
By combining these logical techniques you can solve any Japanese crossword puzzle. Or rather, any crossword puzzle on this site, since there are unsolvable ambiguous Japanese crosswords. But all the scanwords on this site have been checked and are not only solvable, but also allow for a step-by-step solution.
This article is for fans of various puzzles. It will discuss how to correctly solve a Japanese crossword puzzle, and where you can find a huge selection of interesting tasks for free.
History of appearance
The birthplace of the puzzle, as the name suggests, is Land of the Rising Sun. The authorship is still disputed by two representatives of this country. But whoever comes "inventor" this crossword puzzle, puzzle fans all over the world enjoy spending time solving these interesting tasks.
Later, another name for the puzzle appeared - NONOGRAM, on behalf of one of the inventors, a Japanese artist and designer Non Isis. Since the beginning of the 90s, the puzzle began to conquer the European continent, and later - both Americas, Australia and Africa.
In less than a decade nonorgammas are conquering the whole world, Russia does not stand aside either. Puzzles are published in various newspapers and magazines, published as separate brochures and, of course, published on gaming sites on the Internet.
How to solve
The puzzle is a grid of squares. Outside the border of the playing field, horizontally and vertically, there are rows of numbers indicating how many cells in a given line should be painted over. There are two types of puzzles– black and white and color. The algorithm is almost identical for all variations of the crossword puzzle, with minor differences. Let's look at the basic principles of working with nonograms.
Basic principles of the solution
For example, let's take a crossword puzzle with a small picture. (size 13x12 cells), which we will solve later.
So, the solution algorithm:
Rule 1
Between filled cells of the same color there must be at least one empty cell. Explanation for color crosswords – if cells different color there may not be a gap.
Rule 2
For convenience, it is advisable to put a “cross”, “dot” or other small sign in the cells that remain empty (not colored).
Rule 3
It is recommended to cross out the numbers that have already been used to create the drawing. Before we begin the solution, let's carefully study the numbers located on the sides of the field.
Important rules for solving crossword puzzles
Rule 4
If there are values that coincide with the width or height of the field, we begin to paint over them.
In our example, this is the first vertical column (value 12 coincides with the number of cells in height) and the last horizontal line (value 13 is equal to the number of cells in width). Thus, it is necessary to start filling out the drawing with these lines.
Rule 5
If there is no number equal to the number of cells in length or width, you need to find a sequence of numbers whose sum is equal to the length/width of the playing field.
In our example, the first horizontal line falls under this standard: 8 + space + 1 + space + 2 = 13.
If the previous 2 options did not work, then move on to the next option. Let's call it "overlap". The point is this.
Rule 6
We are looking for a sequence whose sum is as close as possible to the number of uncolored cells. We try to virtually draw it first from left to right (or from top to bottom), and then vice versa. Cells that fall into the intersection will be unambiguously shaded. Let's give an example on the penultimate vertical row with the sequence “2;7”. This is not the largest sequence, but it is an option.
Lines 6 to 9 fell into the overlap area - they will be painted over.
Pay attention to the pattern: 2 + space + 7 = 10. The total length of the row is 13 cells. Total 13 – 10 = 3. This indicates that the block of cells is more than 3 pieces. will have an overlap. In example 7 – 3 = 4. We have I got 4 shaded cells.
Rule 7
If there are shaded cells around the perimeter of the field, shade the boundary values.
For our example, let's take a vertical column and fill in all the extreme positions as shown on the slide.
Five more important rules
Rule 8
If there are more empty cells than the length of the last block to be painted, then in the cells that are clearly not painted, we put an empty cell sign (remember about the crosses and dots?).
For clarity, look at the following figure. The shaded sequence must contain 5 elements of which 4 are already shaded. Therefore, on one side You need to paint 1 cell. There are 2 empty fields on the left, 1 on the right. Based on this requirement, the leftmost cell is marked as empty.
Rule 9
If it is impossible to fit a block of cells into an unshaded gap due to length, such a gap will remain empty.
In our example there are two unpainted areas. The length of the first is 4, the second is 2. Only the number 4 remains on the left panel. Therefore, a block of 4 squares will not fit into the second gap. We mark it as the one that will remain empty.
Rule 10
If there is a gap between two nearby cells, filling which will result in a contradiction with the condition of the task, then such a gap must remain unfilled.
In our case, there are two figures of 1 and 2 squares. Between them there is a section that is unknown whether or not to fill. If we color this cell we get a block of 4 cells. But according to the condition, only blocks 1-1-3-1 are possible in this line. Therefore, the available mark the interval as “empty”.
Rule 11
For multi-colored crosswords, in addition to the above, color matching must be observed at the intersection of horizontal and vertical rows.
The example is simple. The extreme color conditions of the first 3 (color green) and last 4 (color blue) columns do not match the color sequence of the block of the last horizontal row. Thus, these cells will be marked as “empty”.
Final Rule
Rule 12
The most important norm. The process of solving a puzzle doesn't have to be a chore. It must provide moral satisfaction.
By following this simple instruction, you can to the fullest enjoy the wonderful world of hand-drawn crosswords.
On this theoretical part The article ends. Let's move on to practical tasks.
Knowing the basic principles of solving a Japanese crossword puzzle, combining them, You can solve nonograms of almost any complexity. As you gain experience, you will develop your own style and methods of solution. Each subsequent puzzle will be solved faster and easier than the previous one. But it’s still advisable to start from simple drawings.
Solving black and white crosswords
To consider the main canons of the crossword puzzle solutions were chosen 2 easy tasks: one is black and white, the other is color. Let's solve them by applying 12 golden rules for solving.
We start with a mono-color crossword puzzle. The first step consists of applying Rules No. 4(the length of the block is equal to the width or length of the field). At the same time, do not forget to cross out the numbers corresponding to the drawn blocks (Rule No. 3). Look at the slide below.
The next step is to draw blocks around the perimeter of the field (Rule #7). We draw blocks horizontally on the left with 8, 2, 1, 1, 1, 2, 2, 1, 1, 1 and 2 cells. Vertically fill the cells at the bottom for 2, 1, 1, 3, 4, 4, 4, 2, 1, 1, 7, 8 squares. Don't forget to mark the end of the blocks.
pay attention to important detail. In vertical rows No. 3 and 9 (counting from the left edge) All the necessary cells have been drawn. Therefore, we mark the remaining ones with a cross, they will be without filling.
Having drawn the indicated sequences, we see that 2 sides have the opportunity to fill boundary blocks. This is the top side and the side right. Let's complete the necessary drawings.
Just a few touches left to do complete solution tasks. Please note that On the upper horizontal line, 4 cells remain unpainted. According to the task, there should be blocks with 1 and 2 cells 1 + 2 = 3. But we remember that between blocks of the same color there must be at least one empty cell. Total 3 +1 = 4!!!
We finish filling out the field and get the desired image.
Colored nonograms
A distinctive feature of such puzzles is multicolor. When solving it, it is necessary not only to correctly arrange the sequence of cells, but also to color them in the colors required, according to the conditions. The wrong color will ruin all your efforts. You should also remember the first condition - Between shaded cells one There must be at least one empty color; if the cells are of different colors, there may be no gap.
All of the above affects appearance crossword– not just numbers are written along the edge of the field, these cells also contain the color that should be used when drawing.
As in the case of a black and white nonogram, let's look at filling out a color puzzle step by step. The initial field size is 14x14 and contains 8 colors.
The algorithm for solving such a puzzle is identical to that used in black and white. Conducting description of Rule No. 11, One of the options for starting the task was given. Using the same norm as well as the property "overlap" Let's start solving it in a different way.
In the 12th line horizontally the values of the numbers are 4 + 2 + 1 + 4 = 11. The field length is 14. Thus, a sequence of more than 3 (14 – 11) can be reflected on the field. Draw a blue cube. Since this is the only figure in the vertical row, we mark the remaining cells of the 11th row vertically with “x”.
As you already understand, you can start drawing in several ways. The result does not change, only the duration of the procedure and its complexity change. Agree, it is easier to determine the boundaries of color sequences than to calculate areas of overlap. But, we repeat, all comes with experience.
Continuation of the crossword puzzle
Draw on the bottom horizontal row block of 6 squares. Next, let's draw the boundary blocks. Let us mark with the symbol “x” those positions where there will be no drawing.
At the next stage, let's pay attention to the 7th vertical row. Taking into account already colored positions 12 cells remain. We check the initial condition 1 + 5 + 2 + 2 + 2 = 12. Feel free to paint the whole row in the colors specified by the condition.
We consistently fill in the boundary values, not forgetting to cross out the used numerical values and placing an “x” in the identified places. We apply the learned habits and combine them We use it to solve the nonogram.
As a result, we will get a wonderful parrot and a lot of positive emotions. It took just under 3 minutes.
Now you can safely start independent decision Japanese puzzles. Below is an overview of the most popular resources containing free crossword puzzles.
Top services with crosswords
For fans of nonograms, as well as those who decided to try their hand at solving Japanese puzzles, our rating of sites on a given topic that provide big choice puzzles.
"Japanese crosswords"
First place in the TOP 5 is the resource of the same name “Japanese crosswords”. The site contains order 20,000 crosswords of varying complexity and topics. The user can choose both mono-color and color options of various sizes and complexity.
A distinctive feature of the site is the name of the puzzles. The user sees only the serial number of the task, without knowing what will be shown in the picture. This creates a certain intrigue when making a decision.
A convenient interface, timer and advanced settings for displaying the progress of the solution, along with a large database of nonograms, certainly determine the primacy of the resource.
GrandGames
Honorary second place We give it to a resource dedicated to puzzles - GrandGames. Unlike the leader of the rating, the resource is not dedicated to exclusively Japanese crossword puzzles. There are other puzzles here too.
A large database (up to 10,000 different tasks) of Japanese puzzles, a convenient search menu, a nice interface and advanced customization options make the resource silver medalist of our TOP parade.
Have you noticed that in Lately many people around you began to solve not ordinary, but Japanese crosswords? And there is an explanation for this. Regular crosswords and their lighter version - scanwords - have not forced you to strain your intellect for a long time. The same formulations like “3-letter parrot” or “clothing for the walls” migrate from newspaper to newspaper. Boring…
What are the “Japanese” good at? Oh, this is a completely different level, each task is unique, and as a result you get moral satisfaction not from the fact that you remembered all the words you know, but from the fact that you saw a picture drawn by you yourself, and the more complex the crossword puzzle, the more detailed the details will be drawn all its details.
The rules for solving such crossword puzzles are not complicated. Let's study? So…
The Japanese crossword is a picture encrypted using numbers. The numbers opposite each row (column) indicate the number of shaded cells in that row (column). If more than one number is written in a row, this means that in this row (column) there are several groups of filled cells, between which there is at least one unshaded cell. The order of the numbers coincides with the order of the shaded groups. Your goal is to determine the location of all groups of numbers on the field and as a result get a picture. There can only be one solution to a crossword puzzle, so if something doesn’t add up, we go back a step and carefully check all our steps. That's all the rules.
Everything seems to be simple. But in practice many questions arise. In magazines and newspapers that publish Japanese crossword puzzles, very primitive pictures are given as examples. And it often happens that you can’t solve any of the proposed options on your own. Therefore, I propose to start learning from the example of a more complex picture, for example, 15x15 cells in size.
1. We start by searching for the largest number, or group of numbers. This is the line with the number 14.
We count 14 cells from left to right and put a point. We repeat the countdown from right to left and also put a point. We connect them and paint over the entire group. We ended up with 13 shaded cells. We don’t yet know where the 14th cell will be - on the right or on the left.
2. Repeat the countdown for the line with the number 9, also from left to right and vice versa. Paint 3 cells:
3. Now let's look at the very bottom line with the numbers 8 and 4. This entry means that in this line there is a group of 8 cells, then a gap of at least one cell, and a group of 4 cells. Let's try to calculate them.
From left to right we count 8 cells, put a dot, skip one cell and continue counting 4 cells. Let's put an end to it. Now from right to left: count 4 cells (dot), skip one and count 8 cells (dot). We connect the points belonging to the eight and four in pairs, and we get groups of 6 and 2 cells. Let's paint them over. It is still unknown in which direction each of the groups will continue.
Please note that when we calculate several groups in a row or column, we always skip 1 intermediate cell, although after completing the solution you will see that there are sometimes more of them. But we will always use this calculation mechanism if we want everything to work out. Let's move on.
4. We apply the same counting algorithm to the line “4 - 7”. You should end up with groups of one and four cells - these are pieces from 4 and 7, respectively.
5. Now let's look at the overall picture:
Pay attention to the columns. Many of them end with the number 1. This means that the lowest group of cells in these columns is equal to one. Therefore, in the line “8 - 4” we can safely mark those “ones” that automatically emerged for us, and the “twos” that can be safely completed. At the same time, we remember that between groups of numbers there must be at least 1 unfilled cell and we agree that we will mark such cells with crosses. Such cells will not be painted over under any circumstances.
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6. Next, let's do it ourselves:
- column “2-1-6-2” - after the bottom “two” there is a “six”. We count 6 cells and paint it completely. Everything came together naturally here. At the end of the group, do not forget to put a cross;
- column “1-3-5-2” - we do the same with the “five”;
— line “9” — we have two filled cells closer to the right edge. From there we count 9 cells, put a dot and connect it to a group of 2 cells. Let's color it in and see that we have 7 out of 9 shaded cells. Since we have only one group in this line, we leave 2 cells free from its supposed left edge, and mark the rest with crosses. There will be nothing there in any case;
— we check the vertical and notice the “threes” that appear (columns “1-1-3-1”, “1-3-1-3-1” and “2-1-2-3-1”), paint them over and not we forget to separate them with crosses;
- in the line “1-6” we count the “six”: from right to left we count six cells (dot) and from the cross from left to right also 6 cells and put a dot. Let's connect, paint over 5 out of 6 cells. We don’t pay attention to the “one” in this line for now;
— we also recalculate the line “7-1”, as a result we paint over 6 out of 7 cells;
- do the same actions with lines “1-5” and “7”;
- then check the verticals and draw the groups that start immediately after the crosses. After each move, check how the picture changes, complete the positions that appear. You should end up with an intermediate picture like this:
In the process of solving, think logically. If in the line “1-6” there is only one position left for one, then it is also part of the “two” from the first column. Therefore, leave room for the completion of the “two”, and mark the rest of the column with crosses. Now you can finish line “14” and count the rows and columns again, marking with crosses those positions where there cannot be any filled cells. Complete the line “4-1-1”, recalculate the columns “1-3-5-2” and “1-3-1-3-1”, and then think logically and be careful, all the cells will appear with each next step . As a result, we got a drawing of a mouse in a shoe.
I congratulate you on your first success!
I hope you enjoyed it and will join our ranks of Japanese crossword puzzle fans!
The images in the Japanese crossword are encrypted using numbers. The numbers are located to the left and top of the main playing field. The numbers show how many cells need to be painted.
In black and white crosswords, two colors are used: white is the color of the main playing field and black is the color with which the player paints the cells. Filled cells must be separated by at least one unfilled cell. For convenience, the playing field is divided into 5 by 5 blocks by a thick line.
The numbers above the playing field show how many shaded cells there should be in each column.
The numbers to the left of the playing field show how many shaded cells there should be in each line.
Basic requirements for a Japanese crossword:
- A crossword puzzle must have only 1 solution, i.e. all painted cells can be calculated logically.
- The number of rows and columns must be a multiple of 5
- There should be no rows or columns with empty cells.
Basic steps to solve
When solving a crossword puzzle you need:
- Find cells that will definitely be shaded
- Find cells that definitely will not be painted
- Color cells whose number positions are precisely known
Example of a Japanese crossword solution
Let's try to solve a simple Japanese crossword "Letter":
The size of the crossword is 10 by 7. Let's try to solve it.
First, let's find all the cells. The first and last lines contain the number 10, which means the entire line will be completely filled in. Also in the first and last column there is the number 7, which means the entire column will be completely filled in. Let's color in these rows and columns and cross out the corresponding numbers.
Now let's take a closer look at the second and 6th lines. These numbers have starting and ending shaded cells. Accordingly, we can continue or complete them.
Now let's mark with crosses those cells where they definitely cannot be painted over
Look at lines 3 and 7. Because There must be one empty cell between the shaded cells and there are the first two shaded cells, we can shade the rest
Most people don't seem to need much instruction on how to solve puzzles Japanese crosswords (broken down by number or nonograms, griddlers, hanjie, picross or whatever you like to call them). The basic solution method is easily demonstrated in a simple example, for example, on the first page of this site. I expect what's most reasonable smart people can understand this without even being shown. And this basic solving technique is actually quite powerful and can be used to solve most puzzles. However, there are some cases where solving the puzzle requires slightly more complex logic tricks.
This page is intended to give some ideas about fancy methods of solving nonograms, and also to establish some terminology for discussing solutions in the forums on this site.
Linear solution
"Linear solution" is when you work with one row or one column at a time. Sometimes it's simple and straightforward, as in the case below, where we know that cells labeled "A" should be black:Example 1.
Sometimes you need to think a little about different cases eg in the case below where the single cell "B" should be black:
Example 2.
And sometimes there are things that are pretty damn hard to spot, like the fact that cell "C" in the row below should be white:
Example 3.
But while solving a line isn't always "simple" in the sense of simplicity, it at least always involves looking at just one row or column at a time.
By the way, computer programs, written to solve number puzzles, support the line of the line. This is what the computer loves - looking at one not most problems at the same time and hoping that a common solution will emerge from it. Puzzles allowed only linear solution, are almost always easily resolved by computers. This is where you have to look at most of the puzzle to understand that people can actually deploy computer programs.
Symmetry
Here's a symmetrical puzzle (warning to compulsive solvers: this doesn't look like anything when it's solved. It's just an example of symmetry.):
Example 4.
The linear solution doesn't get you anywhere in this puzzle.
But the puzzle is symmetrical, in the sense that it is exactly the same as a mirror image. Each horizontal key is reversible. "1 1" back - "1 1". The top key in column 1 is the same as column 4, and the top key in column 2 is the same as column 3.
Obviously, if you found the solution to this puzzle and mirrored the solution around a vertical axis, then that mirror image would also be the solution to the puzzle. If there is only one solution, then we know that the solution must be symmetric. Knowing that the solution is symmetric is a really big key.
Unfortunately, on this website at least, you can never be sure that a puzzle really only has one solution, and not knowing that solving the problem using symmetry is a bit of a cheat. We generally don't consider a puzzle to be "logically solvable" if it can only be solved by symmetry. The exception is that if the puzzle author puts some information in the title of the puzzle like "[has only one solution]", then it is perfectly legal to use symmetry to solve the puzzle because that information was provided to be used as a piece of the puzzle.
Once you know that the solution to the puzzle above is symmetrical, it is trivial to solve it. First, if any side key has an odd number of identification numbers in it (for example, rows "2"), then the center columns must be black. And if he has even number key numbers, then the central columns should be white. (In this case we have two central columns, but if the puzzle has an odd number of columns, we will only have one.) This is enough for solutions to most symmetrical puzzles.
Of course, there are other forms of symmetry. The puzzle may have vertical symmetry or diagonal symmetry, or rotational symmetry (although it must be square for either of the latter two).
While the symmetry solution is a bit of a cheat, it's certainly not the case that it's only looking at one row at a time. You really have to look at the whole puzzle to detect symmetry.
Color logic
The most obvious type of logic that involves looking at rows and columns at the same time is “color logic.” This happens in multi-color puzzles when the row clue tells you that a cell must be either color A or color B, while the column clue tells you it must be either color B or color C, so we can conclude, that it should be color B.Here's a simple example:
Example 5.
Again, linear logic doesn't work, but it's pretty obvious that cell "A" should be white. After all, the row hint says it can only be red or white, and the column hint says it can only be green or white, so it must be white.
Here's more complex example:
Example 6.
Again, solving the line doesn't get us anywhere, and we'll ignore the rotational symmetry of the puzzle (which is hard to understand and trick).
The production line of reasoning, however, is to ask which cells in the second row could be red. Looking at the main clues, we see that the cells marked "A" cannot be red. They may be green or white, but not red. But if that's the case, then cell "B" must be red and can be marked red because every place that red three can include that cell. The same logic can be applied on the other three sides of the puzzle, and once you do this, the rest of the puzzle is easy to solve by solving the line.
The color logic trick remembers what colors each cell can have. Some computer programs, such as the "checker" used on this site, store a list of possible colors for each cell. If you do this, then all the above puzzles are easy to solve with a simple normal solution (although the string solving algorithm becomes a little more complex). Perhaps you could come up with some kind of notation that would allow you to do the same thing on paper, but I doubt that would really be useful. In practice, it's just a matter of figuring it out in your head. It's hard, but I don't think example 6 is really more difficult than, say, example 3.
Boundary logic
"Boundary Logic"(or "Edge logic") is a logic trick often useful around the edges of a puzzle. Puzzle #23 on this site was designed as an example of this kind of thing. It looks like this:
Example 7a
It's hard to imagine a puzzle that's less accessible to line solving. Experienced solvers will immediately notice one promising feature: along the bottom edge there is quite big number(“4”) with small numbers (“2”) on the next line up.
The trick in such cases is to consider the two lines together. Since the "4" line is right at the edge of the puzzle, it is easy to understand what the consequences are if the "4" is in different places and check if those consequences match the "2" line. So we just mentally try “4” in different positions. We could start with the assumption that cell "A" was black. Obviously, this would mean that all cells labeled "B" would also have to be black. Looking at the column hints, we see that the two cells labeled "C" should also be black. Although the cells labeled "D" should be white. But this makes it impossible to sample blacks and whites in this line. There can only be two on this line. So this means that "A" cannot be black and must be white.
Once you get the hang of it, it's pretty easy to see that most places where you could place four in the bottom row would create an impossible pattern in the second row from the bottom. In this puzzle there is actually only one place that can be, and that is the position shown below. In any other position he would either have given three blacks in the second row, or two blacks with a white between them.
Example 7b
If we want to continue solving this puzzle, we will use the same trick again. This time we will be working with the 4 in column 6. Although in this case we are not working with the outer edge of the puzzle, we are still doing the same basic thing at the edge of the unknown area.
Edge logic is useful in a lot of puzzles, but it usually doesn't work as well as in example 7. Often you'll find that there are several different places where an edge block can exist. But this may still be enough so that you can arrange multiple cells (especially in the corners), and it may be that all possible positions overlap on several cells, which you can paint black.
There are many variants of edge logic. Sometimes the first line inside may not be useful, but the second line inside will be more useful. Sometimes you can even apply it to placing a block on the first line inward, checking for consistency with the second line inward.
A good first puzzle to try edge logic is #6336.
Smile logic
Another pattern that is often seen is "smile". We call it because the most common form it appears in is the smile-shaped puzzle below:
Example 8.
The solution shown on the right is unique, but none of the methods described above allow us to solve it (well, symmetry, but we don't want to use symmetry).
The key to it is all those listed in the column tooltips. We know that each column can only have one black color, so we know that horizontal blocks 1 and 2 can never overlap each other. Since the 1s can't be next to each other (because we need empty space between them), blocks of two lines must alternate. They should go 1,2,1.
The same reasoning applies to the puzzle below, with a solution that looks more like a snake than a smile:
Example 9.
Usually puzzles don't start with so many columns containing only one. This is rather the kind of situation that sometimes develops in a puzzle that is almost complete, where there were many other key numbers in the columns, but they have already been placed. Smile logic is something that is typically used at the end of the solution process, as opposed to edge logic, which can be applied at any point. (But for an exception to this rule, see Glamor #6542).
Another common variation of smile logic occurs in situations such as the puzzle below:
Example 10.
This puzzle is already partially solved using the classic line solution, but the line solution does not give us any further results. But the eight unexpanded squares are indeed in the same situation as the basic smile pattern in example 8. The same arguments can be applied to solve this problem.
Two-way logic
The example below is similar to one I once used when I got stuck. I don't have a really clever name, but this moment I call this “two-way logic.” This has been decided as the line decision will take you. What's not so obvious is that all cells labeled "A" must be white.
Example 11.
The reasoning goes like this. Obviously, block "2" in column 7 can only be in one of two positions. This tells us about column 6: either the cell directly above the dotted cell or directly below the dotted cell must be black. So the "2" in this column can only be in one of two positions, which do not contain any "A" cells, so we can arrange them. From there, the rest of the puzzle is easily solved. (In fact, example 11 is not all that cleverly designed, because it can also be solved using edge logic).
So the basic idea here is to look for places where you know that one of the two cells should be black. For each case, think about just a move or two to see what other cells you could install in that case. If in both cases any cells are set the same, you can mark them.
A slightly different example of the same trick is shown below. Using two-way logic on the two open cells in column seven allows you to set exactly one cell, which allows you to solve the rest of the puzzle:
Example 12.
Did you find it? This is the cell in the fourth row and sixth column, and it should be white. If the "2" in column seven is in the top position, then the rest of the fourth row must be white. If "2" is in the down position, the top half of column six should be white. In any case, one cell must be white.
Again, it happens that this puzzle can also be solved using edge logic. It's difficult to deal with small puzzles that can only be solved with bidirectional logic.
Summing up
Sometimes interesting things can be achieved by adding up the number of cells that need to be installed in a certain region. Here's a contrived puzzle to demonstrate this trick:
Example 13.
We used a simple line solution to fill a lot of space, but we have unexplored areas at the top and the bottom is still to be seen. The next thing we would naturally try to complete this puzzle would be edge logic on 12 in the first column, but that doesn't get us anywhere.
But there is a simple trick that will tell us exactly where 12 should be. First, use the row hints to add the number of cells that are needed in the top three rows. The first line is 1 + 2 + 1 = 4, the second is 2 + 2 + 1 = 5, and the third is only 2, so total number equals 4 + 5 + 2 = 11. We need a total of 11 black squares in the top three rows of the puzzle.
Now if we look at the column hints, we can use them to determine the number of cells in the top three rows for each column except the first column. Column 2 should have 2 cells, and the other eight columns should have one each, for a total of 10.
So, since the row hints tell us that there should be 11 cells at the top, and since we know that there are 10 in columns 2 through 10, there should be exactly one black cell in the first three rows of column 1. tells us exactly where 12 should be in column 1, and the rest of the puzzle is trivial to solve.
I've only ever used this trick in a few puzzles, but it's great when it works.
Conclusion
Obviously, this is not an exhaustive list of all the fantastic logic tricks that are useful in solving Japanese crossword puzzles. Sometimes you need to invent a new whole cloth to solve a puzzle. But hey, it's fun, isn't it?Of course, some people prefer solve crosswords just guessing if the situation will be tough. If that makes you happy, then I'm fine.
